Interface

induced lateral
anisotropy of semiconductor
heterostructures
M.O. Nestoklon,
Ioffe Physico

Technical Institute, St. Petersburg, Russia
JASS 2004
Contents
•
Introduction
•
Zincblende semiconductors
•
Interface

induced effects
•
Lateral optical anisotropy: Experimental
•
Tight

binding method
–
Basics
–
Optical properties in the tight

binding method
•
Results of calculations
•
Conclusion
Motivation
The light, emitted in the (001) growth
direction was found to be linearly polarized
This can not be explained by using the T
d
symmetry of
bulk compositional semiconductor
P
lin
(001)
Zincblende semiconductors
T
d
symmetry determines bulk semiconductor
bandstructure
However, we are interested in
heterostructure properties.
An (001)

interface has the lower symmetry
Zincblende semiconductors
The point symmetry of a single (001)

grown
interface is C
2v
C
A
C
’
A
’
Envelope function approach
Electrons and holes with the effective mass
The Kane model takes into account complex band structure of the valence band
and the wave function becomes a multi

component column.
The Hamiltonian is rather complicated…
Zincblende semiconductor
bandstructure
Rotational symmetry
C
n
has n spinor representations
C
2v
contains the second

order rotational axis C
2
and
does not
distinguish
spins differing by 2
For the C
2v
symmetry, states with the spin +1/2 and

3/2 are coupled in the Hamiltonian.
If we have the rotational axis C
∞
, we can define the angular momentum component
l
as a quantum number
l
= 0,
±
1,
±
2,
±
3, …
l
=
±
1/2,
±
3/2, …
The angular momentum can unambiguously be defined only for
l
= 0,
±
1,
±
2,
±
3, …
l
=
±
1/2,
±
3/2, …

n/2
<
l
≤
n/2
Crystal symmetry
As a result of the translational symmetry, the state of an electron in a crystal is
characterized by the value of the wave vector
k
and, in accordance with the Bloch
theorem,
In the absence of translational symmetry the classification by
k
has no sense.
Let us remind that
k
is defined in the first Brillouin zone. We can add any vector
from reciprocal lattice.
Examples

X coupling occurs due to translational symmetry breakdown
J. J. Finley
et al, Phys. Rev. B,
58
,
10 619
, (1998)
Schematic representation of the band
structure of the p

i

n GaAs/AlAs/GaAs
tunnel diode. The conduction

band minima
at the
and X points of the Brillouin zone
are shown by the full and dashed lines,
respectively. The X point potential forms
a quantum well within the AlAs barrier,
with the

X transfer process then taking
place between the

symmetry 2D emitter
states and quasi

localized X states within
the AlAs barrier.
hh

lh mixing
E.L. Ivchenko, A. Yu. Kaminski, U. Roessler,
Phys. Rev. B
54
,
5852
, (1996)
Type

I and

II heterostrucrures
The main difference is that interband optical transition takes place only at the interface
in type

II heterostructure when, in type

I case, it occurs within the whole CA layer
Type I
Type II
Lateral anisotropy
type I
type II
P
lin
(001)
Optical anisotropy in ZnSe/BeTe
A.
V. Platonov, V. P. Kochereshko,
E. L. Ivchenko
et al., Phys. Rev. Lett.
83
, 3546 (1999)
Optical anisotropy in the InAs/AlSb
F. Fuchs
,
J. Schmitz and N. Herres,
Proc. the 23rd Internat. Conf. on Physics of Semiconductors
,
vol.
3
,
1803
(Berlin, 1
996
)
Situation is typical for type

II
heterostructures.
Here the anisotropy is ~ 60%
Tight

binding method: The main idea
C
C
A
C
A
A
Tight

binding Hamiltonian
…
…
…
…
Optical matrix element
The choice of the parameters
The choice of the parameters
In
?
As
?
Al
Sb
Al
?
?
In
As
In
As
?
?
In
As
V
Electron states in thin QWs
GaAs
(strained)
GaSb
GaSb
A.A. Toropov, O.G. Lyublinskaya, B.Ya. Meltser,
V.A. Solov’ev,
A.A. Sitnikova, M.O. Nestoklon, O.V. Rykhova,
S.V. Ivanov
, K. Thonke and R. Sauer,
Phys. Rev
B, submitted (2004)
Lateral optical anisotropy
Results of calculations
E.L. Ivchenko and M.O. Nestoklon, JETP
94
, 644
(
2002
);
arXiv
http://arxiv.org/abs/cond

mat/0403297
(submitted to
Phys. Rev.
B)
Conclusion
•
A tight

binding approach has been developed in order
to calculate the electronic and optical properties of
type

II heterostructures.
•
the theory allows a giant in

plane linear polarization
for the photoluminescence of type

II (001)

grown
multi

layered structures, such as InAs/AlSb and
ZnSe/BeTe.
Electron state in a thin QW
The main idea of the symmetry
analysis
If crystal lattice has the symmetry transformations
Then the Hamiltonian is invariant under these transformations:
where is point group representation
Time inversion symmetry
Basis functions
•
Для описания экспериментальных данных необходим
–
учёт спин

орбитального расщепления валентной зоны
–
для описания непрямозонных полупроводников
“
верхние орбитали
”
(
s*
)
~
20

зонная модель. 15 параметров
Hamiltonian matrix elements
Optical matrix elements
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